Two-stream cyclotron wave amplifier



Oct. 10, 1967 c. K. BIRDSALL TWO-STREAM CYCLOTRON WAVE AMPLIFIER 2 Sheets-Sheet 1 Filed June 8, 1964 uck 1 M irraz/vins' Oct 1967 c. K. BIRDSALL. 19

TWO-STREAM CYCLOTRON WAVE AMPLIFIER Filed June 8, 1964 2 Sheets-Sheet 2 I NV E NTOR.

FIG -3 Can/a5: 445/0054 irroiwir United States Patent 3,346,819 TWO-STREAM CYCLOTRON WAVE AMPLIFIER Charles K. Birdsall, Lafayette, Calif., assignor to The Regents of The University of California, Berkeley, Calif., a corporation of California Filed June 8, 1964, Ser. No. 373,385 4 Claims. (Cl. 330-44) ABSTRACT OF THE DISCLOSURE The invention disclosed and claimed herein relates to apparatus for interacting cyclotron waves of one electron beam with synchronous Waves of another electron beam travelling together at different velocities along a magnetic field. Interaction for the purpose of extremely highfrequency amplification is accomplished by establishing an exciting electric field in the :path of the beams, with the excitation frequency being particularly related to mean and relative electron-drift velocity, as well as cyclotron frequency.

The present invention relates generally to dual stream interaction microwave amplificaion devices, and is more particularly directed to a device of this type wherein amplification is obtained through interaction between cyclotron and synchronous waves of two electron streams traveling in the same direction with different drift velocities.

Traveling wave tubes, double stream plasma amplifiers, and the like, have long been employed in the amplification of microwave signals. However, these devices have not been particularly well suited to the amplification of signals of 100 or more gigacycles (one gigacyle= c.p.s.) having wavelengths of the order of a millimeter, or fraction thereof. Previously, extremely tiny circuits having an extreme criticality of dimensions, or devices employing extremely intense electron streams, were required to accomplish amplification at the foregoing frequencies. For example, conventional double stream spacecharge-wave amplifiers have depended upon longitudinal interaction between fast and slow space charge waves of the respective electron streams, and the operating frequency has been a function of the plasma frequency of the electron streams. More particularly, the operating frequency of double stream space-charge-wave amplifiers is generally limited by the expression:

3 vmean n relative where w is the operating frequency of the device, u is the plasma frequency, vmean is the mean velocity of the two electron streams, and vrelative is the relative velocity of the two electron streams. Inasmuch as plasma frequency is given by:

velocities. In this case the operating frequency is limited by the expression:

fizL

B being the flux density of a magnetic focusing fieldthrough which the electron streams are traveling. It will, thus, be noted from this expression that the operating frequency of the cyclotron wave interaction device of the present invention is primarily limited by the flux density of the magnetic focusing field. For flux densities of practicable magnitudes, for example, of the order of 10 gauss, it will be seen that operating frequencies of the order of gigacycles are easily attained. In accordance with the general aspects of the invention, a magnetic field is generated in an evacuated interaction region into which two well coupled electron streams are directed with different velocities substantially along the field lines. Within the interaction region means are provided to generate an oscillating electric field transverse to the magnetic field at a signal frequency of the order of, or much larger than, the cyclotron angular frequency of electrons for the particular flux density of the magnetic field generated in the interaction region. The oscillating electric field can excite four waves in each of the electron streams, namely, fast and slow cyclotron waves and rightand left-hand polarized synchronous waves. As these waves can have angular or azimuthal variations, they are referred to by azimuthal mode number, m. In the invention hereof ]m]=l is implied although Im| l is allowed. As the electron streams continue through the interaction region, cyclotron and synchronous waves of the respective streams interact to produce a wave of increasing intensity. Output means are disposed in the interaction region at a position longitudinally displaced from the input means in the direction of stream motion and are coupled in energy transfer relation to the streams to thereby extract an amplified signal from the wave of increasing intensity resulting from the interaction between the cyclotron and synchronous waves of the respective streams. It will, thus, be appreciated that the amplifier of the present invention is elfective to amplify microwave signals, and the frequency of these signals may be of the order of 100 or more gigacycles with the employment of electron streams of relatively low density and magnetic focusing fields of practicable magnitudes.

The invention, together with further advantages and possible objects thereof, will be better understood upon consideration of the following detailed description of a preferred embodiment thereof with reference to the accompanying drawings, wherein:

FIGURE 1 is a transverse sectional view of a preferred embodiment of the two-stream cyclotron wave amplifier of the present invention, electrical components being illustrated in schematic;

FIGURE 2 is a transverse sectional view taken at line 2-2 of FIGURE 1; and

FIGURE 3 is a plot of angular frequency versus phase constant of the two electron streams of the amplifier graphically depicting regions of interaction between the synchronous and cyclotron waves of the respective streams.

As noted hereinbefore, the present invention utilizes to good advantage the interaction between cyclotron and synchronous waves of two electron streams traveling at diiferent velocities in the same direction as opposed to conventional dual stream amplification devices which heretofore have generally utilized the interaction between the space-charge-waves of the respective streams to produce amplification. More particularly, two well intermixed electron streams are directed into a magnetic field with different drift velocities v and v parallel to the field and an oscillating electric field is applied to the streams transverse to the magnetic field with an angular signal frequency w. The drift velocities v and v of the respective electron streams are selected such that their mean velocity,

and relative velocity, v (v, =v v are related to the signal angular frequency w and the cyclotron angular frequency w for electrons in the magnetic field of the particular magnitude employed, by the following expressron:

waves are transverse velocity waves in contrast to the syn-.

chronous waves which are transverse displacement waves. More particularly, the cyclotron waves arise from electrons rotating about the magnetic field lines with the cyclotron frequency ar and simultaneously translating in the longitudinal direction with the drift velocity of the particular electron stream, v in the case of the slow stream and v in the case of the fast stream. The cyclotron waves may, accordingly, be visualized by imagining a string of electrons glued to a cylinder in the form of a helix and the cylinder to be rotating at the cyclotron frequency w and translating in the longitudinal direction with hte drift velocity of the particular electron stream. However, as viewed by a fixed observer facing the longitudinal direction, different electrons that appear to be a single electron are seen to rotatewith the apparent frequency w. However, for a slow cyclotron wave, the pitch of the spiral of electrons is positive whereas for the fast cyclotron wave, the pitch is negative. Accordingly, a fixed observer facing in the longitudinal direction from which the electron streams arrive, sees the fast and slow cyclotron waves rotate respectively in opposite directions with the apparent frequency m. In fact, it can be shown that the sense of rotation of the slow cyclotron wave is such that same is righthand polarized, while the sense of rotation of the fast cyclotron wave is such that same is left-hand polarized. With regard to the individual electron streams, it should be noted that for the slow stream of drift velocity v the phase constant of the fast cyclotron wave is given by 5 p while the phase constant of the slow cyclotron wave excited therein is given by: B a-B where Similarly, for the fast stream at drift velocity v the fastcyclotron wave excited therein has a phase constant which is given by ,8 [3 and the slow cyclotron wave excited therein has a phase constant given by fi -i-p where Considering now the synchronous Waves of the respective electron streams in greater detail, as noted above a synchronous wave is essentially a transverse displacement wave and the electrons associated with such a synchronous wave therefore do not have transverse velocity, although successive electrons are transversely displaced relative to each other. More particularly, a synchronous wave may be likened to the motion of water sent out from a garden hose nozzle that is rotated, provided gravity is neglected. Thus, each electron follows a straight line trajectory in the longitudinal direction, but successive electrons lie on a spiral. There are two synchronous waves of this variety for each electron stream, the difference between the two synchronous waves being that successive electrons of one wave lie on a left-hand wound spiral, while electrons of the other wave lie on a right-hand wound spiral. The phase velocity of each synchronous wave of the respective streams is equal to the drift velocities of the streams, i.e., the velocity v for the slow stream and the velocity v; for the fast stream. Thus, a fixed observer facing in the longitudinal direction for each stream sees two synchronous waves wherein different electrons as time progresses for the respective waves appear as single electrons rotating respectively in clockwise and counterclockwise directions with the angular frequency w. Each stream thus has a right-hand polarized synchronous wave and a left-hand polarized synchronous wave. The phase constant of the synchronous waves of the slow electron stream is equal to 8 whereas the phase constant of the synchronous waves of the fast stream is equal to 3 With fast and slow cyclotron waves and leftand righthand polarized synchronous waves of the foregoing type excited in the respective electron streams of drift velocities v and v and these velocities related to the signal frequency w and cyclotron frequency w as described above, various interactions can occur between the waves of the respective streams as the streams progress through the interaction region. More particularly, the fast cyclotron wave of the slow electron stream, which is left-hand polarized, can be made to have a phase constant and angular frequency which are comparable to the. left-hand polarized synchronous Wave of the fast electron stream. Similarly, the slow cyclotron wave of the fast stream, which is righthand polarized, can be made to have a phase constant and angular frequency which are equal to those of the.

right-hand polarized synchronous wave of the slow electron stream. When two waves have the same polarization, phase constant, and angular frequency, the waves interact with each other to produce growing and decaying waves. Thus, under one set of conditions, the fast cyclotron wave of the slow electron stream interacts with the left-hand polarized synchronous wave of the fast electronstream, and under another set of conditions, the slow cyclotron wave of the fast electron stream interacts with the righthand polarized synchronous wave of the slow electron stream, to thereby produce growing and decaying waves. These sets of conditions or regions for interaction are graphically illustrated in the diagram of FIGURE 3 of signal frequency, 0), versus phase constant, ,8, for a relatively fast and a relatively slow electron stream. The slopes of the straight lines depicting the cyclotron and synchronous waves of the fast and slow streams represent the phase velocities of the waves which, as noted previously, are the drift velocities of the respective streams. By virtue of the difference between the velocities of the respective streams, and the difference in the phase constants of the waves induced in each stream for any given value of signal frequency, various of the wave representing lines of one stream intersect various of the wave representing lines of the other stream. In this regard, the line denoting the synchronous waves of the fast stream intersects the line denoting the fast cyclotron wave of the slow stream at point A. Similarly, the line denoting the synchronous waves of the slow stream intersects the line denoting the slow cyclotron wave of the fast stream at point B. These intersection points A and B are,

of course, indicative of the waves represented by the intersecting lines having the same phase constant and angular frequency. The conditions for interaction are fulfilled at points A and B, the further requirement of like polarizations of the waves being satisfied at point A between the left-hand polarized synchronous wave of the fast stream and fast cyclotron wave of the slow stream, and at point B between the right-hand polarized synchronous wave of the slow stream and slow cyclotron wave of the fast stream. Thus, for an angular signal frequency w corresponding to point A the left-hand polarized synchronous wave of the fast stream interacts with the fast cyclotron wave of the slow stream to produce growing and decaying waves. Similarly, for an angular signal frequency m corresponding to point B, the right-hand polarized synchronous wave of the slow stream interacts with the slow cyclotron wave of the fast stream to produce growing and decaying waves. More particularly, in both of the foregoing cases, the bunched electrons of one of the waves periodically slip by those of the other wave, and in so doing generate a decaying wave, which damps out, and a growing wave which is, thus, periodically re-enforced. The electrons helically slip one wavelength of the signal frequency each cycle of the cyclotron frequency such that the frequency of the re-enforced growing wave is equal to the signal frequency. By virtue of the growing Wave, an amplified signal may be derived from the electron streams by suitable output means coupled in energy transfer relation to the electron streams at a position longitudinally displaced from the electric field generating means in the direction of stream motion.

Considering now the two-stream cyclotron wave amplifier, generally outlined hereinbefore in greater detail with respect to the preferred embodiment illustrated in FIG- URE 1, it is to be noted that the interaction region is preferably defined by means of an evacuated envelope 11 having a solenoid 12 disposed concentrically thereabout and energized by a direct current magnet power supply 13 to thereby generate the magnetic focusing field longitudinally through the envelope. At one end of the envelope there are provided a pair of electron guns 14 and 16 which respectively include cathodes 17 and 18 and accelerating electrodes 19 and 21. The cathodes may be, for example, of the indirectly heated variety as shown, with filaments 22 and 23 respectively disposed within the cathodes 17 and 18 to heat same and effect the thermionic emission of electrons therefrom. Heating current is supplied to the filaments by means of a filament power supply 24, or equivalent means, commonly connected thereto. The accelerating electrodes 19 and 21 are preferably in the form of centrally apertured metallic discs in spaced alignment with the cathodes 17 and 18. The axes of the guns 14 and 16 are slightly inclined with respect to the axis of the envelope 11 such that upon the establishment of potential gradients between the accelerating electrodes and cathodes of the respective guns, electrons are directed through the apertures of the accelerating electrodes with radial and longitudinal components of velocity. The elevtron streams of the respective guns are thereby intermixed adjacent the axis of the envelope and focused axially therethrough by the longitudinal magnetic field. The streams from the respective guns have longitudinal drift velocities which are determined by the potential difference between the accelerating electrodes and cathodes thereof. In this regard, different drift velocities are established for the respective streams in accordance with the considerations discussed hereinbefore by providing different potential difference between the accelerating electrodes and cathodes of the respective guns. This may be accomplished by commonly connecting the accelerating electrodes 19 and 21 to a negative terminal 26 of a D-C power supply 27, the positive terminal of which is connected to ground. The cathode 18 of gun 16 is connected to a negative terminal 28 of the supply which is more negative than terminal 26 and the cathode 17 of gun 14 is connected to a negative terminal 29 which is more negative than the terminal 28. Thus, since the accelerating electrodes 19 and 21 are at the same potential, while the cathode 17 is at a more negative potential than the cathode 18, the electron accelerating potential difference between cathode 17 and accelerating electrode 19 is greater than that between cathode 18 and accelerating electrode 21. As a result, the electrons from gun 14 have greater velocity than the electrons from gun 16. Consequently, electron gun 14 produces the fast electron stream, while electron gun 16 produces the slow electron stream previously considered. Preferably a fieldfree region for the drifting electron streams is extended longitudinally through the envelope to a metallic collector 30 at the opposite end thereof from the electron guns and which is preferably connected to ground. Preferably a conducting cylinder 31 is provided at the inside of the envelope 11 and held at constant potential, such as that of anodes 19 and 21, to provide the field-free drift region.

Modulation of the two electron streams traveling with different drift velocities longitudinally through the envelope 11 with a transverse electric field at a predetermined signal frequency may be variously efiected. For example, a pair of transversely spaced-apart plates may be disposed within the envelope on opposite sides of the axis thereof and a radio frequency signal source coupled be tween the plates. More preferably, however, the oscillating transverse electric field is established by means of a Cuccia coupler 32 coaxially disposed within the envelope adjacent the electron guns 14 and 16. As is conventional, the coupler 32 includes a hollow metallic cylinder 33 having axially aligned stream inlet and outlet apertures 34 and 36 at its opposite ends. The cylinder 33 defines a cavity 37 within which a pair of transversely spaced-apart plates 38 and 39 are disposed on opposite sides of the cylinder axis and are in integral connection therewith as by means of stems 41 and 42. An oscillating transverse electric field is established between the plates 38 and 39 upon excitation of the cavity 37 as by means of a radio frequency coupling loop 43 disposed therein and connected by means of a coaxial cable 44 to a radio frequency signal source 46. The signal source has an angular operating frequency to selected in the manner hereinbefore described and the oscillating transverse electric fiel-d oscillates at this frequency to excite the cyclotron and synchronous waves in the electron streams as they pass through the coupler 32.

The output means for extracting energy from the reenforced growing wave of the electron streams and providing an amplified signal is similar to the input means and may, accordingly, be provided as a pair of parallel transversely spaced plates disposed on opposite sides of the envelope axis. Preferably, however, the output means comprises a second Cuccia coupler 47 which includes a closed hollow cylinder 48 coaxially .disposed within the envelope 11 at a position longitudinally displaced downstream from the coupler 32. The cylinder 48 is provided with axially aligned stream inlet and outlet apertures 49 and 51 at its opposite ends and defines a cavity 52 within which a pair of transversely spaced parallel plates 53 and 54 are disposed on opposite sides of the cylinder axis and integrally connected therewith as by means of stems 56 and 57. A radio frequency coupling loop 58, or equivalent means, and coaxial cable 59 are employed to couple the cavity 52 to a radio frequency load 61. The re-enforced wave in the electron streams in traversing the coupler cavity 52 between the plates 53 and 54 establishes an oscillating transverse electric field by condenser action and such field induces the flow of amplified signal current through the load 61.

While the present invention has been described hereinbefore with respect to a single preferred embodiment, it will be appreciated that numerous modifications and changes may be made therein without departing from the true spirit and scope of the invention, and thus it is not intended to limit the invention except by the terms of the following claims.

What is claimed is:

1. A two-streamcyclotron wave amplifier comprising means generating a magnetic field in an evacuated interaction region, means directing two well coupled electron streams respectively having different velocities into said interaction region substantially parallel to said magnetic field, inputmeans generating an electric field in said interaction region transverse to said magnetic field and having a frequency of w defined by the relation wherein v is the mean drift velocity of electrons in the two streams, V is the relative drift velocity of electrons in the two streams and w is the cyclotron frequency of electrons in the streams, to thereby excite synchronous and cyclotron waves in each of said electron streams with a cyclotron wave of one stream interacting with a synchronous wave of the other stream during transit of the streams through the interaction region to produce a wave of increasing intensity, and output means coupled in energy transfer relation to said streams at a position of saidinteraction region displaced from said input means in the direction of stream motion for extracting an amplified signal from said Wave of increasing intensity.

2. A two-stream cyclotron wave amplifier comprising an evacuated envelope, means generating a magnetic field longitudinally through said envelope, electron gun means disposed at one end of said envelope directing two intermixed electron streams through said envelope respectively with different longitudinal drift velocities v and v said streams thereby having a mean velocity and relative velocity v -v said drift velocities v and v being selected such that and E" s Ba, U1

said electric field exciting in said second stream a fast cyclotron wave of left-hand polarization having a phase constant B -p a slow cyclotron wave of right-hand polarization having a phase constant d t-13 and synchronous waves of rightand left-hand polarizations having phase constants B where said fast cyclotron wave having said phase constant fi ,B interacting withsaid synchronous wave of lefthand polarization having said phase constant 5 to produce a re-enforced wave having said frequency w, or said slow cyclotron wave having said phase constant fl 6 interacting with said synchronous wave of right-l1and polarization having said phase constant ,B to produce a re-enforced wave having said frequency w, and transverse coupling means disposed in said envelope in energy transfer relation to said electron streams at a position downstream from said electric field for extracting an amplified signal from said reinforced wave.

3. A two-stream cyclotron wave amplifier according to claim 2, further defined by said means generating an electric field comprising a hollow cylindrical coupler defining a cavity coaxially disposed in said envelope and having axial stream inlet and outlet apertures at its opposite ends, said coupler having integral parallel transversely spaced plates disposed in said cavity onopposite sides of the axis thereof, and a radio frequency signal source coupled to said cavity to induce a transverse electric field therein, and by said transverse coupling means comprising a second hollow cylindrical coupler defining a cavity coaxially disposed in said envelope and having axial stream inlet and outlet apertures in its opposite ends, said second coupler having integral parallel transversely spaced plates disposed in said cavity on opposite sides of the axis thereof, and a load coupled to the cavity defined by said second coupler.

4. A two-strearncyclotron wave amplifier, comprising a cylindrical vacuum envelope, a pair of electron gains disposed in said envelope adjacent one end thereof at ofi axis positions, said electron guns each including a cathode and an accelerating electrode positioned to direct electrons towards the axis of said envelope and longitudinally thereof when a potential is applied between the cathode and accelerating electrode, means for establishing positively increasing potentials of different magnitudes between the cathodes and accelerating electrodes of the respective guns whereby the electron streams therefrom have different drift'velocities, a collector disposed at the opposite end of said envelope from said guns to receive the electron streams therefrom, a direct current energized solenoid concentrically disposed about said envelope to establish a magnetic field longitudinally therethrough, a first hollow cylindrical coupler defining a cavity coaxially disposed in said envelope adjacent said guns and having inlet and outlet apertures in its opposite ends for traversal by said electron streams, said coupler having integral parallel plates disposed within said cavity transversely spaced on opposite sides of the axis thereof, a source of radio frequency energy coupled to said cavity to excite an electric field therein "between said plates, said source having an angular frequency which is approximately equal to the ratio of the mean to relative velocities of said electron streams times the angular cyclotron frequency of electrons in said magnetic field, a second hollow cylindrical coupler defining a second cavity coaxially disposed in said envelope adjacent said collector and having inlet and outlet apertures in its opposite ends for traversal by said electron streams, said second coupler having integral parallel plates disposed within said second cavity transversely spaced on opposite sides of the axis thereof, and an output load coupled to said second cavity for receiving radio frequency energy therefrom.

References Cited UNITED STATES PATENTS 2,912,613 11/1959 Donal et al., 3l55.16 3,054,964 9/1962 Ashkin et al. 3153.5 X 3,218,503 11/1965 Adler 3153 1 3,270,241 8/1966 Vural 315-3 (Other references on following page) 9 OTHER REFERENCES Ashkin: (Energy Interchange Between Cyclotron and Synchronous Waves in Quadrupolar Pump Fields) Journal of Applied Physics, vol. 32, No. 6, 1961, pp. 1137- 1143.

Gordon: (Transverse Electron Beam Waves in Varying Magnetic Field) Bell Sys. Tech. Journal, November 1960, pp. 1603-1616.

Siegman: (Waves on a Filamentary Electron Beam in a Transverse Field Slow Wave Circuit) Journal of Applied Physics, vol. 31, N0. 1, January 1960, pp. 21-25.

HERMAN KARL SAALBACH, Primary Examiner.

ELI LIEBERMAN, Examiner.

S. CHATMON, JR., Assistant Examiner. 

1. A TWO-STREAM CYCLOTRON WAVE AMPLIFIER COMPRISING MEANS GENERATING A MAGNETIC FIELD IN AN EVACUATED INTERACTION REGION, MEANS DIRECTING TWO WELL COUPLED ELECTRON STREAMS RESPECTIVELY HAVING DIFFERENT VELOCITIES INTO SAID INTERACTION REGION SUBSTANTIALLY PARALLEL TO SAID MAGNETIC FIELD, INPUT MEANS GENERATING AN ELECTRIC FIELD IN SAID INTERACTION REGION TRANSVERSE TO SAID MAGNETIC FIELD AND HAVING A FREQUENCY OF A W DEFINED BY THE RELATION 